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Line 23: Every construction of a covering code gives an upper bound on ''K''<sub>''q''</sub>(''n'', ''R''). Lower bounds include the sphere covering bound and ~~Rodemich’s~~Rodemich's bounds <math>K_q(n,1)\geq q^{n-1}/(n-1)</math> and <math>K_q(n,n-2)\geq q^2/(n-1)</math>.<ref>E.R. Rodemich, Covering by rook-domains, ''[[Journal of Combinatorial Theory]]'', 9 (1970), 117-128</ref> The covering problem is closely related to the packing problem in <math>Q^n</math>, i.e. the determination of the maximal size of a ''q''-ary ''e''-[[Error detection and correction\|error correcting]] code of length ''n''.

Covering code: Difference between revisions